34. Information from the American Institute of Insurance indicates the meanamount of life insurance per household in the United States is $110,000. This distribution follows the normal distributionwith a standard deviationof $40,000.

a. If we select a random sampleof 50 households, what is the standard errorof the mean?

b. What is the expected shape of the distribution of the sample mean?

c. What is the likelihood of selecting a sample with a mean of at least $112,000?

d. What is the likelihood of selecting a sample with a mean of more than $100,000?

e. Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000.

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.